Question: #12. Let A be an m x n matrix and B be an n x p matrix. Prove that (a) N(B) CN(AB). (b) C(AB) C

#12. Let A be an m x n matrix and B be an n x p matrix. Prove that (a) N(B) CN(AB). (b) C(AB) C C(A). (Hint: Use Proposition 4.1.) (c) N(B) = N(AB) when A is n x n and nonsingular. (d) C(AB) = C(A) when B is n x n and nonsingular

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